Navigating the complexity of ecological stability
Donohue, I., Hillebrand, H., Montoya, J. M., Petchey, O. L., Pimm, S. L., Fowler, M. S., Healy, K., Jackson, A. L., Lurgi, M., McClean, D., O'Connor, N., O'Gorman, E. J., & Yang, Q. (2016). Navigating the complexity of ecological stability. Ecology Letters, 19(9), 1172–1185. https://doi.org/10.1111/ele.12648
Published in: Ecology Letters
Document Version: Peer reviewed version
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Download date:28. Sep. 2021 1 Navigating the complexity of ecological stability
IAN DONOHUE1,2, HELMUT HILLEBRAND3, JOSÉ M. MONTOYA4, OWEN L. PETCHEY5, STUART L. PIMM6, MIKE S. FOWLER7, KEVIN HEALY1,2, ANDREW L. JACKSON1,2, MIGUEL LURGI8, DEIRDRE MCCLEAN1,2, NESSA E. O'CONNOR9, EOIN J. O'GORMAN10 & QIANG YANG1,2
1School of Natural Sciences, Trinity College Dublin, Ireland 2Trinity Centre for Biodiversity Research, Trinity College Dublin, Ireland 3Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Germany 4 Theoretical and Experimental Ecological Station, CNRS, UPS, Moulis, France 5Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland 6Nicholas School of the Environment, Duke University, Durham, USA 7Department of Biosciences, Swansea University, UK 8Environment Institute and School of Biological Sciences, University of Adelaide, Adelaide, Australia 9School of Biological Sciences, Queen’s University Belfast, Northern Ireland 10Faculty of Natural Sciences, Department of Life Sciences, Imperial College London, UK
Author emails: ID: [email protected]; HH: [email protected]; JMM: [email protected]; OLP: [email protected]; SLP: [email protected]; MSF: [email protected]; KH: [email protected]; ALJ: [email protected]; ML: [email protected]; DM: [email protected]; NOC: [email protected]; EOG: [email protected]; QY: [email protected].
Running head: Navigating the complexity of stability
Keywords: sustainability, disturbance, conservation, policy, resistance, resilience, variability, persistence, invasion, extinction
Type of article: Reviews and Syntheses
Word count: 192 (abstract), 5691 (main text); with four figures, two tables and two text boxes (comprising, respectively, 480 and 356 words).
Number of references: 94
Corresponding Author: Ian Donohue, School of Natural Sciences, Zoology Building, Trinity College, Dublin 2, Ireland. Email: [email protected]. Telephone: +35318961356. Fax: +35316778094.
Author contributions: ID led the project. ID, SLP, JMM, HH and OLP led the writing. ID, DM, QY and OLP analysed the data. All authors contributed to idea development and the writing of the manuscript.
1 2 1 Abstract
2 Human actions challenge nature in many ways. Ecological responses are ineluctably complex,
3 demanding measures that describe them succinctly. Collectively, these measures encapsulate the
4 overall “stability” of the system. Many international bodies, including the Intergovernmental
5 Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES), broadly aspire to
6 maintain or enhance ecological stability. Such bodies frequently use terms pertaining to stability
7 that lack clear definition. Consequently, we cannot measure them and so they disconnect from a
8 large body of theoretical and empirical understanding. We assess the scientific and policy literature
9 and show that this disconnect is one consequence of an inconsistent and one-dimensional approach
10 that ecologists have taken to both disturbances and stability. This has led to confused
11 communication of the nature of stability and the level of our insight into it. Disturbances and
12 stability are multidimensional. Our understanding of them is not. We have a remarkably poor
13 understanding of the impacts on stability of the characteristics that define many, perhaps all, of the
14 most important elements of global change. We provide recommendations for theoreticians,
15 empiricists and policymakers on how to better integrate the multidimensional nature of ecological
16 stability into their research, policies and actions.
2 3 17 Introduction
18 Species live in a web of prey and other resources, mutualists, competitors, predators, diseases,
19 and other enemies (Montoya et al. 2006; Bascompte 2009; McCann & Rooney 2009; Kéfi et al.
20 2012; Tilman et al. 2012). All encounter a profusion of diverse perturbations in their environment,
21 both natural and human-induced, that vary in their spatial extents, periods, durations, frequencies
22 and intensities (Tylianakis et al. 2008; Miller et al. 2011; Pincebourde et al. 2012; MacDougall et
23 al. 2013). These multifaceted disturbances precipitate a range of responses that can alter the many
24 components of ecological stability and the relationships among them (Donohue et al. 2013). This
25 complexity necessitates a multidimensional approach to the measurement of stability. We examine
26 the extent of our understanding of the multidimensional nature of both disturbances and stability.
27 We find that it is highly restricted. Consequently, our ability to maintain the overall stability of
28 ecosystems for different management and policy goals is limited. If ecology is to support and
29 inform robust and successful policy, we must rectify this.
30 At least three scientific communities use terms that map onto various dimensions of
31 ecological stability. Theoreticians, for example, have developed an extensive literature on whether
32 the population dynamics of multi-species systems will be asymptotically stable in the strict
33 mathematical sense (May 1972; Thébault & Fontaine 2010; Allesina & Tang 2012; Rohr et al.
34 2014), or resilient, in the sense of a fast return to equilibrium following a small disturbance (Pimm
35 & Lawton 1977; Okuyama & Holland 2008; Suweis et al. 2013), and other well-defined measures
36 (see, for example, Pimm 1984; McCann 2000; Ives & Carpenter 2007). Empiricists observe and
37 manipulate natural systems or variously perturb experimental ones to measure ecological responses
38 in constant or naturally changing environments (Tilman et al. 2006; O’Gorman & Emmerson 2009;
39 Grman et al. 2010; Carpenter et al. 2011; de Mazancourt et al. 2013; O’Connor & Donohue 2013;
40 Hautier et al. 2014). Finally, many international bodies concerned with environmental conservation
41 aspire to maintain, protect, and sustain nature and avoid altering and degrading it, all for informing
3 4 42 decision makers and aspiring to enrich people’s lives and well-being (Mace 2014; Díaz et al. 2015;
43 Lu et al. 2015).
44 We explore whether the associated three scientific literatures engage each other in using the
45 same terms and employ the same meanings for them when they do. Generally, they do not. We
46 must remedy this. International bodies need terms that are simple and flexible, but surely not to the
47 point of being meaningless. Theory cannot advance usefully in isolation from tests of it (Scheiner
48 2013), and theory, experiment, and observation must sensibly inform decision makers at all levels.
49 Most importantly, the multidimensional complexity of natural responses to environmental change
50 needs to be recognised by all communities, both separately and collectively.
51 We suggest solutions to help achieve these goals. For theoreticians, we provide suggestions
52 on where to focus future research to incorporate the sort of complexities commonly encountered in
53 natural systems. Empiricists will find useful our summary of the methodologies developed so far to
54 study the different facets of ecological stability and our recommendations for better assessing
55 stability in collaboration with theoreticians and policymakers. Finally, we provide suggestions for
56 environmental policymakers on how to develop and frame objectives and targets that are not only
57 relevant for policy but at the same time facilitate much closer links with the supporting, and
58 evolving, science.
59
60 The multifaceted nature of disturbances and ecological responses
61 Disturbances are changes in the biotic or abiotic environment that alter the structure and
62 dynamics of ecosystems. Although they occur at a variety of scales and vary in their direct and
63 indirect effects on species, all disturbances comprise four key properties; their magnitude, their
64 duration, their frequency and how they change over space and time (Sousa 1984; Benedetti-Cecchi
65 2003; García Molinos & Donohue 2011; Pincebourde et al. 2012; Tamburello et al. 2013). The
66 magnitude of a disturbance is defined by how much the aspect of environmental change departs
67 from its undisturbed state (i.e. “a measure of the strength of the disturbing force”; Sousa 1984). A
4 5 68 minor storm versus a once in 100-year hurricane is an example of disturbances that vary in
69 magnitude. Their duration refers to a continuum with instantaneous pulses — short, sharp
70 shocks — and sustained presses — constant, long-term change — at the ends of the spectrum (Fig.
71 1a). A discrete pollution event, such as a chemical spill, is a pulse, and the extinction of a species
72 from an ecosystem is a press. Theoreticians focus primarily on one of these two extremes of the
73 duration gradient (Ives & Carpenter 2007). Empiricists sometimes refer to these extremes as acute
74 and chronic disturbances, respectively.
75 Natural disturbance regimes are clearly more complicated than this. Changes in the
76 magnitude, duration and frequency of disturbances over time or in space can combine to give
77 disturbances directionality (Fig. 1b). Directionality measures the trajectory of change, which can be
78 highly dynamic and variable in terms of its mean and variance. Both can elicit distinct ecological
79 responses (Bertocci et al. 2005; Benedetti-Cecchi et al. 2006; García Molinos & Donohue 2010,
80 2011; Pincebourde et al. 2012; Mrowicki et al. 2016). Many of the most globally important
81 disturbances in nature are of this kind (Fig. 1c). Therefore, while a focus on pure pulse or press
82 disturbances provides some important insight into mechanisms that can underpin biological
83 responses to disturbances, the relevance of this to predicting responses to real disturbances in the
84 natural world may be limited.
85 While the multifaceted nature of disturbances creates a problem for assessing, understanding,
86 and predicting how ecological systems respond (García Molinos & Donohue, 2010; Mrowicki et al.
87 2016), the ecological responses themselves are also complex. Ecological stability is a
88 multidimensional concept that tries to capture the different aspects of the dynamics of the system
89 and its response to perturbations. Pimm (1984) reviewed five components of ecological stability
90 that are in common use. Asymptotic stability is a binary measure describing whether a system
91 returns asymptotically to its equilibrium following small disturbances away from it. One measures
92 variability, the inverse of stability, as the coefficient of variation of a variable over time or across
93 space. Persistence is the length of time a system maintains the same state before it changes in some
5 6 94 defined way. It is often used as a measure of the susceptibility of systems to invasion by new
95 species or the loss of native species. Resistance is a dimensionless ratio of some system variable
96 measured after, compared to before, some perturbation. Resilience is the rate at which a system
97 returns to its equilibrium, often measured as its reciprocal, the return time for the disturbance to
98 decay to some specific fraction of its initial value. Systems with shorter (faster) return times are
99 more resilient than those that recover more slowly. Holling (1973) introduced another definition of
100 resilience that is currently in common use, particularly in policy fora (Walker et al. 2004; Hodgson
101 et al. 2015). It “is a measure of the persistence of systems and of their ability to absorb change and
102 disturbance and still maintain the same relationships between populations or state variables.” This
103 definition is multidimensional. It integrates persistence, resistance and the existence of local
104 asymptotic stability at multiple equilibria. It has come to mean whether or not a system returns to
105 its former equilibrium following disturbance or moves to another one. This idea may be expanded
106 further to compare systems in terms of what range of disturbances a system can withstand before
107 being shifted to a new equilibrium (Ives & Carpenter 2007). If there is a limit beyond which a
108 system cannot return directly to its former state, this is termed a tipping point.
109 The different components of stability are all based in some way on the composition, function
110 and dynamics of communities. They are unlikely to be independent. Furthermore, the strength and
111 even the nature of relationships among stability components can change when communities are
112 disturbed in different ways (Donohue et al. 2013). This complexity has critical implications for our
113 understanding of the impacts of disturbances on ecosystems. It means that restricting our focus to
114 single measures of stability in isolation, or to amalgamated ones such as Holling’s resilience, when
115 they are used to reduce the multidimensional complexity of stability to a single dimension and its
116 measurement to a single number, risks significantly underestimating the impacts of perturbations. It
117 also risks incomplete understanding of the mechanisms that underpin the overall stability of
118 ecosystems. The multidimensionality of ecological responses demands explicit multidimensional
119 measurement of both disturbances and stability.
6 7 120 The definitions of the various components of stability all come with underlying assumptions
121 about the nature of ecosystems and the disturbances that affect them. Measures of variability, for
122 example, commonly assume the presence of stationary fluctuations [i.e. without an underlying
123 directional trend (Tilman et al. 2006; Loreau & de Mazancourt 2013)]. The ecological definitions of
124 resilience (Quinlan et al. 2016) argue for different worldviews, one where a single equilibrium
125 dominates, the other where two or more equilibrium domains are possible, with tipping points
126 between them. The Aichi Targets (UN 2010) that consider “safe ecological limits” may invoke the
127 latter view, as do related concepts, such as planetary boundaries, that are the subject of considerable
128 debate (Box 1). Other definitions may read into a simpler notion of, for example, preventing
129 overexploitation. Irrespective of definitions, theoretical studies of stability are generally based on
130 the dynamics of communities at, or very close to, some form of equilibrial state. Given the highly
131 dynamic nature of the natural world and the strong directionality of many elements of global
132 change, this limits the applicability of existing theory to the real world and creates significant
133 challenges for empiricists trying to test its predictions.
134
135 What do ecologists measure?
136 To understand the differences in what theoreticians and empiricists study, we surveyed three
137 high impact multidisciplinary journals and four leading general ecology journals: Nature, Science,
138 PNAS, Ecology Letters, Ecology, Oikos and American Naturalist. Using relevant search terms
139 (“ecolog* stability”; “ecolog* resilience”; “ecolog* resistance”; “stability and diversity”), this
140 yielded 894 papers, 354 of which measured ecological stability in one or more ways. About half of
141 these studies were purely theoretical, the other half empirical. Of the latter, there were nearly equal
142 proportions of experimental and observational studies. Only 4% of papers combined both theory
143 and empirical measurement.
144 In our survey, 93% of theoretical studies and 85% of experimental and observational studies
145 focus on a single facet of stability (Fig. 2a). Some 83% of theoretical studies and 80% of
7 8 146 experimental and observational studies also focus on only a single disturbance component (Fig. 2b).
147 This demonstrates a restricted, largely one-dimensional, perspective. It means that we have little
148 understanding of either the multidimensional nature of ecological stability or the correspondence of
149 different components of stability to different types of perturbations.
150 There is also a significant disjoint between theoretical and empirical approaches to, and
151 understanding of, ecological stability. The majority (57%) of theoretical studies focus on
152 asymptotic stability, whereas experimental (61%) and observational (72%) studies concentrate
153 primarily on variability (Fig. 3a). In contrast, asymptotic stability comprises the focus of only 4%
154 of empirical studies, while only 18% of theoretical studies quantified variability. Only a small
155 minority of studies, either theoretical or empirical, examine persistence (10% of studies), resilience
156 (7%) or resistance (7%). Within these latter three measures, there are notable differences.
157 Theoretical studies most often examine persistence, resilience and a particular measure of resistance
158 called robustness – the susceptibility to species extinctions, usually caused by the initial loss of a
159 species (Solé & Montoya 2001; Staniczenko et al. 2010). Observational studies emphasise
160 resistance, while experimental studies consider resistance and resilience in equal measure. Our
161 survey identified very few empirical studies of robustness. Additional aspects of stability are
162 potentially addressed in more specialized journals than those scanned in our survey. However, the
163 literature we surveyed came from the general ecological journals most probably read by both
164 theoreticians and empiricists, potentially making the divergence we found in terms and concepts
165 even more significant.
166 We found similar disparities between the focus of theory and empirical research on the
167 different types of disturbance durations and frequencies. The majority (70%) of theoretical studies
168 focus on the effects of single pulse perturbations on stability (Fig. 3b). In contrast, 83% of
169 observational studies examine the effects of combined, multiple pulse disturbances (Fig. 1a),
170 usually in the form of natural environmental fluctuations. Experimental studies prioritise the effects
171 of press and multiple pulse disturbances in broadly equal measure (respectively, 38% and 47%).
8 9 172 Only 15% of studies we surveyed incorporate the effects of disturbance magnitude. The problem is
173 more acute when we account for different components of stability. For example, our survey
174 identified no theoretical studies of the effects of disturbance magnitude, pulse or multiple pulse
175 disturbance frequencies on ecological resistance. Nor did we find any experimental or observational
176 studies of the effects of pulse disturbances on asymptotic stability (Fig. S1). In spite of its
177 importance to characterising disturbances in the real world, our survey identified only one study
178 (van Nes & Scheffer 2004) that explored the effects of the directionality of a disturbance on
179 ecological stability.
180 Almost exclusively, just two characteristics of communities provide the basis upon which
181 studies measure ecological stability. Population or community biomass comprises the focus of
182 approximately two-thirds (63%) of studies included in our survey, while almost all of the remaining
183 studies (35%) examine the stability of taxonomic composition in some way (Fig. 3c). This pattern is
184 broadly consistent across both theoretical and empirical studies and across all components of
185 stability, except for persistence, where the majority of studies focus on composition, and
186 robustness, whose definition is constrained to community composition (Fig. S2). We found few
187 (six) studies that measured the resilience of community composition.
188 In spite of the strong policy focus on ensuring the sustained provision of ecosystem services
189 (e.g. TEEB 2010; Díaz et al. 2015), we found remarkably few empirical or theoretical assessments
190 of the stability of related ecosystem functions or processes. Only 2% of studies in our survey
191 examined the stability of an ecosystem function or process, in spite of their importance to the
192 perceived economic value of ecosystems (Armsworth & Roughgarden 2003). Of those, almost all
193 measured the variability of ecosystem function in time or space. We found only one study (Zavaleta
194 et al. 2010) that also examined thresholds for the persistence of multiple functions. Our survey
195 identified no studies of the resilience, asymptotic stability or resistance of ecosystem functions.
196 There is significant bias towards terrestrial ecosystems (52%) among empirical studies of
197 stability, of which most (53%) are from grasslands. Of the remaining studies, 29% are from
9 10 198 freshwater ecosystems, while only 16% are from marine systems. Experimental and observational
199 studies are represented approximately equally across all ecosystem types.
200 What are the conclusions we draw from this? Clearly, experimentalists and empiricists can
201 estimate the clearly-defined measures used by theoreticians. The problem is that some things are
202 easy to measure and other things not, a distinction that likely leads to the differences we have noted.
203 The differences are even greater on closer inspection: theory does not always address what
204 empiricists can measure. This is, at least in part, because the mathematics of dynamical systems
205 lacks tools for evaluating quantities of interest to empirical ecologists. Take resilience, for example.
206 Models measuring resilience use the engagingly simple idea of asymptotic stability. They calculate
207 return times over long intervals — when transient changes have decayed — and close to the
208 equilibrium — where one can use linear approximations to the underlying non-linear nature of the
209 system (Pimm 1982). Empiricists, on the other hand, tend to look at short intervals and disturbances
210 far from the equilibrium, where transient effects in the models may be significant (De Vries et al.
211 2012; Hoover et al. 2014; O’Connor et al. 2015). Here, the simplifying mathematics are
212 unavailable, and so are ignored. The models may still provide broadly the right insights, but there is
213 no guarantee that they do. Theoreticians could take the extra step and explore the dynamics of their
214 models over short intervals away from equilibrium, even if only using simulations, to check their
215 generality (e.g. Hastings 2004; Ives & Carpenter 2007; Ruokolainen & Fowler 2008). More
216 generally, theoreticians might recognise that certain aspects of their theories are far more likely to
217 be tested — and to be more widely useful — if they addressed metrics that empiricists can more
218 easily measure (Shou et al. 2015).
219 A more fundamental problem arises from the lack of exploration of the multidimensional
220 nature of either disturbances or stability. This gap in knowledge limits our ability to understand and
221 predict the effects of disturbances on the overall stability of ecosystems. If the science of ecology is
222 to support and inform robust and successful policy, we should close this gap.
223
10 11 224 The goals of policy and their measurement
225 Many consequences of human actions on nature are simple and have clearly defined units.
226 For instance, the United Nations Convention on Biological Diversity (CBD) and related
227 conventions sets targets that include the numbers of species and areas of habitat to be protected, and
228 rates of extinction, habitat loss and fragmentation, and overexploitation of fisheries and rangelands
229 to be minimised (UN 1992). Assisting developing countries reduce carbon emissions from
230 deforestation and forest degradation is the simply stated goal of the United Nations REDD
231 (Reducing Emissions from Deforestation and Forest Degradation in Developing Countries)
232 Programme (UN 2008). These may neither be easy to measure in practice nor to manage
233 effectively, but they do not pose conceptual challenges.
234 Much more problematic are associated terms. Sustainability is ubiquitous (Bosch et al. 2015),
235 and has a large associated literature. For some, it is used in a normative way, that is, as some
236 desired goal or set of goals. Thus, it is part of the mission of the Global Environment Facility
237 (GEF), and about half of the CBD’s Aichi Biodiversity Targets for 2010-2020 include the word
238 (UN 2010). IPBES includes conservation and sustainability of ecosystem services to provide long-
239 term human well-being in its conceptual framework (Díaz et al. 2015). Responsibilities of the UK
240 Department for Environment, Food and Rural Affairs include sustainable development, which
241 China adopted explicitly as a national strategy in 1996 (Chinese Ministry of Finance et al. 2014).
242 Most commercial enterprises now include statements about corporate and environmental
243 sustainability in their mission statements. Normative definitions of sustainability therefore play an
244 important role in policy, and environmental decision makers clearly do not only concern themselves
245 with ecological components of stability. But neither should they ignore them.
246 We defer to the Oxford English Dictionary that defines “sustainable” as “the quality of being
247 sustainable at a certain rate or level” and environmentally sustainable as “the degree to which a
248 process or enterprise is able to be maintained or continued while avoiding the long-term depletion
249 of natural resources.” Following this, we take sustainability (in its non-normative sense) to mean
11 12 250 that a particular resource persists, or persists above (or below) some pre-determined level, or is
251 resistant to disturbances. Its translation to ecological concepts is conceptually straightforward.
252 Other terms are less so. For example, the 20 Aichi Targets include: safe ecological limits
253 (Targets 4 & 6), degradation (Target 5), function (Targets 8, 10 & 19), and integrity (Target 10)
254 (UN 2010). These terms lack definitions, or have more than one definition, and have no clear units
255 for quantification. This imprecision is unfortunate in itself (Bosch et al. 2015; Lu et al. 2015). It
256 also denies the integration of the large body of empirical and theoretical literature that deals with
257 broadly similar, but quantifiable, measures of multi-species systems that might provide key
258 insights.
259 Differences among terms used, and in the meanings of common terms (Grimm et al. 1992;
260 Grimm & Wissel 1997; Ives & Carpenter 2007; Hodgson et al. 2015), are likely a consequence of
261 the different goals of theoretical and empirical ecologists and policymakers and practitioners. They
262 also reflect the fact that ecologists have perhaps less influence on these terms and their use than we
263 might hope. These differences create significant challenges for translating research findings into
264 policy-relevant information, for communication among individuals from different groups, and for
265 dealing with the complexity and multifaceted nature of ecological stability. We now examine the
266 terms used by policymakers and practitioners, then explore the potential for common ground.
267
268 How do ecologists and policymakers differ in the terms they use?
269 We surveyed policy targets and mission and vision statements of 42 key international
270 agreements, organisations and agencies (Table 1) that are concerned primarily with the conservation
271 and protection of nature. We searched for terms that are associated positively with stability. The
272 most common terms we found were, by some distance, ‘sustain’ and ‘sustainability’. These were
273 present in more than half of the targets and statements examined (Table 2). They occurred almost
274 twice as frequently as the next most common terms, ‘conserve’ and ‘conservation’. We identified
275 14 other terms that occurred less frequently across the documents we examined (Table 2). Of all of
12 13 276 the terms we identified, only two, ‘stabilise’/‘stable’ and ‘resilience’/‘resilient’, have clear
277 ecological definitions. Unfortunately, their use in the documents implied different meanings to
278 those widely used in ecological theory, relating most strongly to, respectively, variability and
279 resistance.
280 In spite of the widely different terminologies used by ecologists and policymakers and
281 practitioners, all of the terms we identified in policy targets and statements could be associated in
282 some way with at least one, and frequently more than one, component of ecological stability (Table
283 2). In fact, the stability components that associate most strongly with these terms are among the
284 least studied by ecologists (Fig. 3a). For some terms, the link with components of stability was
285 clear, for others less so. For example, to ‘constrain impacts’ necessitates increasing the resistance of
286 systems to disturbances. It also implies increasing their resilience (i.e. reducing their return times).
287 The fact that the majority of the terms used in policy integrate across different components of
288 ecological stability means that they are also, at least implicitly, multifaceted. ‘Sustainable’ is a good
289 example of this. In order to be sustainable, ecosystems must be resistant to disturbances. They must
290 recover quickly from them (i.e. have high resilience). This implies that at least some properties (e.g.
291 primary production) remain relatively unchanged through time (i.e. have high robustness, low
292 variability) even though there may be considerable turnover in other properties (e.g. species
293 composition; indeed, it may be the turnover in species composition that results in sustainable
294 primary production).
295 Thus, key terms may lack unambiguous and clear definitions, and are not therefore directly
296 quantifiable. Yet, the widespread use of such holistic terms implies that the multidimensionality of
297 ecological stability is already integrated, even if unconsciously, in the language and targets of
298 policymakers. This observation provides the motivation for closer integration with the science of
299 ecology.
300
301 Solutions and recommendations
13 14 302 Nature responds to human pressures in complex ways. Conversely, political and governance
303 decisions often demand simplicity (OECD 2001; Harwood & Stokes 2003; Lu et al. 2015).
304 Acknowledging this dilemma is a first step towards enhancing the quality of the communication of
305 “stability” at the science-policy interface and within both science and policy. It is incumbent upon
306 ecologists to ensure that this process does not dilute the integrity of the underlying science.
307 The necessary second step involves the definition of terms and their measurement. There is a
308 fundamental need for interdisciplinary discussions about both of these (Box 2). Policymakers have
309 to attach measurable quantities to the terms used in their documents, while scientists must address
310 these concepts directly in their studies. The proliferation of undefined and, indeed, unmeasurable
311 ideals, such as many of the tasks that underpin the recently published United Nations Sustainable
312 Development Goals (SDGs) for the conservation of ecosystems (Goals 14 and 15), hinders progress
313 and is self-defeating. For example, SDG Task 14.2 sets the target that, “By 2020, (countries will)
314 sustainably manage and protect marine and coastal ecosystems and avoid significant adverse
315 impacts, including by strengthening their resilience”. This statement is ambiguous to the point of
316 being meaningless. Not a single aspect of this target is measurable. What constitutes “significant”?
317 What does resilience mean in this context? The goals of policy and the terminology used to describe
318 them always need to be defined and measurable.
319 Consider two examples from the Aichi Targets that contrast how measureable are their
320 aspirations. First, Aichi Target 11: “By 2020, at least 17 per cent of terrestrial and inland water,
321 and 10 per cent of coastal and marine areas…are conserved through effectively and equitably
322 managed, ecologically representative and well connected systems of protected areas”. These goals
323 are explicit and measureable, but those for Aichi Target 6 are not: “By 2020 all fish and
324 invertebrate stocks and aquatic plants are managed and harvested sustainably…so that … fisheries
325 have no significant adverse impacts on threatened species and vulnerable ecosystems and the
326 impacts of fisheries on stocks, species and ecosystems are within safe ecological limits”. This
327 statement contains three particularly obscure terms that lack clear methods for measurement –
14 15 328 sustainably, significant adverse impacts and safe ecological limits – each of which appears to mean
329 two distinct things. As used in this context (see also Table 2), sustainably has a compositional
330 aspect – that species present in the system persist – and another related to biomass stability – that
331 variability of biomass at both population and community level is minimised at least to a level that
332 ensures the persistence of species. Significant adverse impacts requires that the persistence of both
333 ‘threatened species’ and the functioning of ‘vulnerable ecosystems’ is ensured, while safe
334 ecological limits requires ensuring the persistence of each of the biomass, composition and
335 functioning of ecosystems, presumably by enhancing their resistance to fishing activities.
336 Removing the obscure terms and replacing them with the clearly defined ones we suggest would
337 make the goal measureable. This would enable closer links with the supporting science and
338 highlight key research needs, which, in turn, make the goal attainable.
339 For their part, scientists need to take a coherent approach to quantifying stability, such as the
340 one we describe here. The field will not advance by publishing more, partly overlapping, definitions
341 of single terms used in isolation within a discipline. We need to employ broadly accepted terms and
342 apply them consistently across different communities. Both theoreticians and empiricists also need
343 to be more explicit about the basis upon which they are measuring stability. Conclusions drawn
344 about the factors that drive biomass resilience, for example, are likely to be very different from
345 those that underpin compositional resilience.
346 The third step is crucial. Both scientists and policymakers need to recognise that the
347 multidimensional nature of environmental change always requires a multidimensional assessment
348 of responses. To date, scientists and policymakers alike have tended to assess the response to one
349 driver of change using one aspect of stability or amalgamated concepts such as Holling’s resilience.
350 The hope is that this strategy provides a piece of the jigsaw that, in total, provides insight into the
351 overall complexity of responses. Rather, such simplification blurs the overall picture. For example,
352 increasing temporal variability of algal biomass may indicate transient dynamics in changing lake
353 food-webs (Carpenter et al. 2011). It tells us little about any underlying changes in community
15 16 354 structure that may be undermining, or indeed enhancing, resistance to different kinds of
355 disturbances. The one-dimensional approach to disturbances and stability means that we
356 underestimate the impacts of perturbations and cannot identify the mechanisms that underpin the
357 overall stability of ecosystem structure or functions. The existence of trade-offs (i.e. inverse
358 correlations) between different components of stability exacerbates this situation. Such trade-offs
359 exist in nature (Donohue et al. 2013) and there is some theoretical insight into why they occur
360 (Harrison 1979; Loreau 1994; Dai et al. 2015). Their existence has profound implications for
361 policymakers and practitioners, necessitating decisions on which aspects of stability to prioritise for
362 different management goals. They also provoke an environmental cost to those decisions, where
363 some aspects of ecological stability are necessarily diminished to enhance others. The lack of
364 exploration of the multidimensional nature of ecological stability means that our ability to optimise
365 the overall stability of ecosystems for different management and policy goals is at present
366 extremely limited.
367
368 What science is needed to support these steps and enhance the efficacy of policy?
369 We make three recommendations. First, the necessity for improved and mechanistic insight
370 into the multidimensional nature of disturbances and stability requires more realistic theory and
371 experimental designs and an improved ability to integrate across studies from different spatial and
372 temporal scales and different kinds of ecosystem (e.g. Peters et al. 2011). Even single pulse
373 disturbances (e.g., a chemical spill) often have a legacy (e.g., contamination, loss of rare species)
374 that corresponds to a press disturbance. Pulse and press disturbances likely affect different
375 components of stability in different ways. Likewise, many press disturbances exhibit clear
376 directionality and dynamic variation around the mean, with single extreme events occurring more
377 frequently. For instance, the nature of climate disruption calls for new theory (Ives et al. 2010;
378 Stenseth et al. 2015) and long-term experiments. These need to consider the incrementally
379 increasing magnitude of, for example, temperature change, and the possibility of including large
16 17 380 variability up to extreme climatic events. They must employ stability metrics that do not require
381 strong equilibrium assumptions (e.g. fixed point attractors). Moreover, they must be able to
382 evaluate ecosystems in continuous transient dynamics (Fukami & Nakajima 2011). The research of
383 theoretical and empirical ecologists has to include the complex nature of disturbances and stability,
384 and the result of such multidimensional approaches has to inform policymakers.
385 Some existing theoretical approaches may be extended to deal with this range of natural
386 complexity. For example, Floquet theory can be used to explore the stability properties of periodic
387 (cyclical, non-single point equilibrium) systems (e.g. Lloyd & Jansen 2004, Klausmeier 2008). This
388 can be developed in a similar way to assess how locally stable, single point equilibria respond to
389 perturbations. Lyapunov exponents can be used to investigate more complex, chaotic intrinsic
390 dynamics in naturally variable systems (Ellner & Turchin 1995). Gao et al. (2016) have proposed
391 general methods that can reduce the high dimensionality of multi-species systems to predict the loss
392 of resilience (defined there as the ability to avoid switching from a relatively high to much lower
393 mean value of a focal state variable). In parallel, new theoretical developments are starting to
394 explore links between what empiricists measure (e.g. variability) and what theoreticians analyse
395 (e.g. asymptotic resilience), showing that some fundamental relationships can be established
396 (Arnoldi et al. 2016). Together, these approaches offer promising new directions for further
397 theoretical research that incorporate the sort of complexities empiricists commonly encounter in
398 their study systems.
399 Second, we need simple, yet scientifically sound, ways to integrate across the multiple
400 dimensions to quantify the overall stability of ecosystems. These methods will need to distil the
401 most important elements of stability and make accurate quantitative measures on each dimension.
402 Only then can we combine them (Fig. 4). These methods also need to be adaptable to the priorities
403 of specific policies. Such adaptation is fundamental to optimising the overall stability of ecosystem
404 structure and/or functioning for different management and policy objectives. Agricultural
405 management, for example, aims to minimise variability of yield production and maximise
17 18 406 resistance of biomass to pathogens and insect pests. In contrast, many conservation programs might
407 try to maximise the compositional persistence and resilience of communities (rare species are often
408 the most endangered and they tend to determine the slowest return times of the system). Such semi-
409 quantitative methods of holistic assessment may seem too broad-brush and inaccurate to satisfy
410 many scientists. They may also be too complex for some policymakers. The solution has to be
411 something that sits between the two.
412 Third, we need to evaluate and monitor stability through space and time. Ecologists have
413 experience in doing this for single populations and key functional groups (e.g. Ives et al. 2008;
414 Carpenter et al. 2011) and, more recently, for monitoring changes in the provision of ecosystem
415 goods and services (Tallis et al. 2012). Monitoring the dynamic stability of whole networks has
416 largely been the province of economists, among others, with numerous financial stability
417 monitoring programs continuously tracking sources of systemic risk (Adrian et al. 2014).
418 Analogous programs for monitoring the dynamic multidimensional stability of whole ecological
419 systems over time and space are essential to help assess the effectiveness of policy and management
420 actions. These programmes are needed to help identify ecosystems whose stability is being
421 compromised in the face of global change.
422
423 Conclusions
424 There are policies concerned with the protection of nature that set defined and measurable
425 targets. Aichi Target 5 (UN 2010) constitutes a good exemplar: “By 2020, the rate of loss of all
426 natural habitats, including forests, is (to be) at least halved and where feasible brought close to
427 zero”. This statement is clear and unambiguous – progress can be quantified, success or failure
428 evaluated. It exemplifies the only way that policies can effect meaningful change.
429 Such policies are in the minority. Many policy documents describe targets that may appear,
430 on face value, explicit and measurable, yet contain terms that are ambiguous, or have multiple
431 definitions that mean different things to different people. Such targets cannot be connected to
18 19 432 measureable ecological processes or properties. Policies aiming to increase “resilience” provide
433 pervasive examples. In fact, the majority of policy documents we surveyed contain goals using
434 terms that lack definition within ecology. Such ambiguity paralyses policy.
435 This incoherence is, at least in part, a consequence of the inconsistent and one-dimensional
436 approach that ecologists have taken to ecological stability. This approach has led to confused
437 communication of the nature of stability and the level of our insight into it. Disturbances and
438 stability are multidimensional. Our understanding of them is not. We have a remarkably poor
439 understanding of the impacts on stability of the characteristics that define many, perhaps all, of the
440 most important elements of global change.
441 The solution requires a range of actions. We need more realistic theory based on measures
442 that are of practical significance and empirically quantifiable. Empiricists need to test this theory at
443 a range of spatial and temporal scales. Policymakers need to use these defined and measurable
444 quantities in their targets. Most importantly, theoreticians, empiricists, policymakers and
445 practitioners each need to incorporate the multidimensional complexity of natural responses to
446 environmental change into their research, policies and actions.
447
448 Acknowledgements
449 A UK NERC/BESS Tansley Working Group award supported this study. We thank Stefano
450 Allesina, David Raffaelli and an anonymous reviewer for their insightful comments, which helped
451 to improve the quality of this manuscript. DM was funded by a Postgraduate Award from Trinity
452 College Dublin. QY was funded by a postgraduate scholarship from the Irish Research Council. KH
453 was funded by the Earth and Natural Sciences (ENS) Doctoral Studies Programme, funded by the
454 Higher Education Authority (HEA) through the Programme for Research at Third Level
455 Institutions, Cycle 5 (PRTLI-5), co-funded by the European Regional Development Fund (ERDF).
456 OLP was supported by SNF project 31003A_159498 and the University of Zurich Global Change
457 and Biodiversity Research Priority Programme. HH received funding from the German Science
19 20 458 Foundation (DFG Hi848 18-1). JMM was supported by the TULIP Laboratory of Excellence
459 (ANR-10-LABX-41; ANR-11-IDEX-0002-02) and by the Region Midi-Pyrénées (CNRS 121090).
460
461 References
462 1.
463 Adrian, T., Covitz, D. & Liang, N. (2014). Financial stability monitoring, Staff Report No. 601,
464 Federal Reserve Bank of New York.
465 2.
466 Allesina, S. & Tang, S. (2012). Stability criteria for complex ecosystems. Nature, 483, 205-208.
467 3.
468 Armsworth, P. R. & Roughgarden, J. E. (2003). The economic value of ecological stability. Proc.
469 Natl. Acad. Sci. U.S.A., 100, 7147-7151.
470 4.
471 Arnoldi, J.-F., Loreau, M. & Haegeman, B. (2016). Resilience, reactivity and variability: A
472 mathematical comparison of ecological stability measures. J. Theor. Biol., 89, 47-59.
473 5.
474 Bascompte, J. (2009). Disentangling the web of life. Science, 325, 416-419.
475 6.
476 Benedetti-Cecchi, L. (2003). The importance of the variance around the mean effect size of
477 ecological processes. Ecology, 84, 2335-2346.
478 7.
479 Benedetti-Cecchi, L., Bertocci, I., Vaselli, S. & Maggi, E. (2006) Temporal variance reverses the
480 impact of high mean intensity of stress in climate change experiments. Ecology, 87, 2489-2499.
481 8.
482 Bertocci, I., Maggi, E., Vaselli, S. & Benedetti-Cecchi, L. (2005). Contrasting effects of mean
483 intensity and temporal variation of disturbance on a rocky seashore. Ecology, 86, 2061-2067.
20 21 484 9.
485 Bosch, R., van de Pol, M. & Philp, J. (2015). Define biomass sustainability. Nature, 523, 526-527.
486 10.
487 Byrnes, J. E. K., Gamfeldt, L., Isbell, F., Lefcheck, J. S., Griffin, J. N., Hector, A. et al. (2014).
488 Investigating the relationship between biodiversity and ecosystem multifunctionality: challenges
489 and solutions. Methods Ecol. Evol., 5, 111-124.
490 11.
491 Cardinale, B. J., Matulich, K. L., Hooper, D. U., Byrnes, J. E., Duffy, E., Gamfeldt, L. et al. (2011).
492 The functional role of producer diversity in ecosystems. Am. J. Bot., 98, 572-592.
493 12.
494 Cardinale, B. J., Duffy, J. E., Gonzalez, A., Hooper, D. U., Perrings, C., Venail, P. et al. (2012).
495 Biodiversity loss and its impact on humanity. Nature, 486, 59-67.
496 13.
497 Carpenter, S. R., Cole, J. J., Pace, M. L., Batt, R., Brock, W. A., Cline, T. et al. (2011). Early
498 warnings of regime shifts: a whole-ecosystem experiment. Science, 332, 1079-1082.
499 14.
500 Chinese Ministry of Finance, Chinese Ministry of Foreign Affairs, Chinese Ministry of Science and
501 Technology, Chinese Ministry of Environmental Protection, Chinese National Development and
502 Reform Commission & Guo, L. C. (2014). The People’s Republic of China National Report on
503 Sustainable Development. ICP Intercultural Press.
504 15.
505 Dai, L., Korolev, K. S. & Gore, J. (2015). Relation between stability and resilience determines the
506 performance of early warning signals under different environmental drivers. Proc. Natl. Acad. Sci.
507 U.S.A., 112, 10056-10061.
508 16.
21 22 509 de Mazancourt, C., Isbell, F., Larocque, A., Berendse, F., De Luca, E., Grace, J. B. et al. (2013).
510 Predicting ecosystem stability from community composition and biodiversity. Ecol. Lett., 16, 617-
511 625.
512 17.
513 De Vos, J. M., Joppa, L. N., Gittleman, J. L., Stephens, P. R. & Pimm, S. L. (2015). Estimating the
514 normal background rate of species extinction. Conserv. Biol., 29, 452-462.
515 18.
516 De Vries, F. T., Liiri, M. E., Bjørnlund, L., Bowker, M. A., Christensen, S., Setälä, H. M. et al.
517 (2012). Land use alters the resistance and resilience of soil food webs to drought. Nature Clim.
518 Change, 2, 276-280.
519 19.
520 Díaz, S., Demissew, S., Carabias, J., Joly, C., Lonsdale, M., Ash, N. et al. (2015). The IPBES
521 Conceptual Framework—connecting nature and people. Curr. Opin. Environ. Sustain., 14, 1-16.
522 20.
523 Donohue, I., Petchey, O. L., Montoya, J. M., Jackson, A. L., McNally, L., Viana, M. et al. (2013).
524 On the dimensionality of ecological stability. Ecol. Lett., 16, 421-429.
525 21.
526 Ellner, S. & Turchin, P. (1995). Chaos in a noisy world: new methods and evidence from time-
527 series analysis. Am. Nat., 145, 343-375.
528 22.
529 Fukami, T. & Nakajima, M. (2011). Community assembly: alternative stable states or alternative
530 transient states? Ecol. Lett., 14, 973-984.
531 23.
532 Gao, J., Barzel, B. & Barabási, A.-L. (2016). Universal resilience patterns in complex networks.
533 Nature, 530, 307-312.
534 24.
22 23 535 García Molinos, J. & Donohue, I. (2010). Interactions among temporal patterns determine the
536 effects of multiple stressors. Ecol. Appl., 20, 1794-1800.
537 25.
538 García Molinos, J. & Donohue, I. (2011). Temporal variability within disturbance events regulates
539 their effects on natural communities. Oecol., 166, 795-806.
540 26.
541 Grimm, V. & Wissel, C. (1997). Babel, or the ecological stability discussions: An inventory and
542 analysis of terminology and a guide for avoiding confusion. Oecol., 109, 323-334.
543 27.
544 Grimm, V., Schmidt, E. & Wissel, C. (1992). On the application of stability concepts in ecology.
545 Ecol. Model., 63, 143-161.
546 28.
547 Grman, E., Lau, J. A., Schoolmaster, D. R. & Gross, K. L. (2010). Mechanisms contributing to
548 stability in ecosystem function depend on the environmental context. Ecol. Lett., 13, 1400-1410.
549 29.
550 Harrison, G. W. (1979). Stability under environmental stress: resistance, resilience, persistence and
551 variability. Am. Nat., 113, 659-669.
552 30.
553 Harwood, J. & Stokes, K. (2003). Coping with uncertainty in ecological advice: lessons from
554 fisheries. Trends. Ecol. Evol., 18, 617-622.
555 31.
556 Hastings, A. (2004). Transients: the key to long-term ecological understanding? Trends. Ecol. Evol.,
557 19, 39-45.
558 32.
23 24 559 Hautier, Y., Seabloom, E. W., Borer, E. T., Adler, P. B., Harpole, W. S., Hillebrand, H. et al.
560 (2014). Eutrophication weakens stabilizing effects of diversity in natural grasslands. Nature, 508,
561 521-525.
562 33.
563 Hodgson, D., McDonald, J. L. & Hosken, D. J. (2015). What do you mean, ‘resilient’? Trends Ecol.
564 Evol., 30, 503-506.
565 34.
566 Holling, C. S. (1973). Resilience and stability of ecological systems. Annu. Rev. Ecol. Evol. Syst., 4,
567 1-23.
568 35.
569 Hoover, D. L., Knapp, A. K. & Smith, M. D. (2014). Resistance and resilience of a grassland
570 ecosystem to climate extremes. Ecology, 95, 2646-2656.
571 36.
572 Ives, A. R. & Carpenter, S. R. (2007). Stability and diversity of ecosystems. Science, 317, 58-62.
573 37.
574 Ives, A. R., Einarsson, A., Jansen, V. A. A. & Gardarsson, A. (2008). High-amplitude fluctuations
575 and alternative dynamical states of midges in Lake Myvatn. Nature, 452, 84-87.
576 38.
577 Ives, A. R., Abbott, K. C. & Ziebarth, N. L. (2010). Analysis of ecological time series with
578 ARMA(p,q) models. Ecology, 91, 858-871.
579 39.
580 Kéfi, S., Berlow, E. L., Wieters, E. A., Navarrete, S. A., Petchey, O. L., Wood, S. A. et al. (2012).
581 More than a meal... integrating non-feeding interactions into food webs. Ecol. Lett., 15, 291-300.
582 40.
583 Klausmeier, C. A. (2008). Floquet theory: a useful tool for understanding nonequilibrium dynamics.
584 Theor. Ecol., 1, 153-161.
24 25 585 41.
586 Lloyd, A. L. & Jansen, V. A. A. (2004). Spatiotemporal dynamics of epidemics: synchrony in
587 metapopulation models. Math. Biosci., 188, 1-16.
588 42.
589 Loreau, M. (1994). Material cycling and the stability of ecosystems. Am. Nat., 143, 508-513.
590 43.
591 Loreau, M. & de Mazancourt, C. (2013). Biodiversity and ecosystem stability: a synthesis of
592 underlying mechanisms. Ecol. Lett., 16, 106-115.
593 44.
594 Loreau, M., Naeem, S., Inchausti, P., Bengtsson, J., Grime, J. P., Hector, A. et al. (2001).
595 Biodiversity and ecosystem functioning: current knowledge and future challenges. Science, 294,
596 804-808.
597 45.
598 Lu, Y., Nakicenovic, N., Visbeck, M. & Stevance, A.-S. (2015). Policy: Five priorities for the UN
599 Sustainable Development Goals. Nature, 520, 432-433.
600 46.
601 MacDougall, A. S., McCann, K. S., Gellner, G. & Turkington, R. (2013). Diversity loss with
602 persistent human disturbance increases vulnerability to ecosystem collapse. Nature, 494, 86-89.
603 47.
604 Mace, G. M. (2014). Whose conservation? Science, 345, 1558-1560.
605 48.
606 Mace, G. M., Reyers, B., Alkemade, R., Biggs, R., Chapin III, F. S., Cornell, S. E. et al. (2014).
607 Approaches to defining a planetary boundary for biodiversity. Glob. Environ. Chang. 28, 289-297.
608 49.
609 May, R. M. (1972). Will a large complex system be stable? Nature, 238, 413-414.
610 50.
25 26 611 McCann, K. S. (2000). The diversity-stability debate. Nature, 405, 228-233.
612 51.
613 McCann, K. S. & Rooney, N. (2009). The more food webs change, the more they stay the same.
614 Philos. Trans. R. Soc. B-Biol. Sci., 364, 1789-1801.
615 52.
616 Miller, A. D., Roxburgh, S. H. & Shea, K. (2011). How frequency and intensity shape diversity-
617 disturbance relationships. Proc. Natl. Acad. Sci. U.S.A., 108, 5643-5648.
618 53.
619 Montoya, J. M., Pimm, S. L. & Solé, R. V. (2006). Ecological networks and their fragility. Nature,
620 442, 259-264.
621 54.
622 Mrowicki, R.J., O'Connor, N.E. & Donohue, I. (2016) Temporal variability of a single population
623 can determine the vulnerability of communities to perturbations. Journal of Ecology, 104, 887-897.
624 55.
625 Naeem, S., Ingram, J. C., Varga, A., Agardy, T., Barten, P., Bennett, G. et al. (2015). Get the
626 science right when paying for nature's services. Science, 347, 1206-1207.
627 56.
628 O'Connor, N. E. & Donohue, I. (2013). Environmental context determines multi-trophic effects of
629 consumer species loss. Glob Chang Biol., 19, 431-440.
630 57.
631 O'Connor, N. E., Bracken, M. E. S., Crowe, T. P. & Donohue, I. (2015). Nutrient enrichment alters
632 the consequences of species loss. J. Ecol., 103, 862-870.
633 58.
634 O'Gorman, E. J. & Emmerson, M. C. (2009). Perturbations to trophic interactions and the stability
635 of complex food webs. Proc. Natl. Acad. Sci. U.S.A., 106, 13393-13398.
636 59.
26 27 637 OECD (2001). Governance in the 21st Century. OECD Publications.
638 60.
639 Okuyama, T. & Holland, J. (2008). Network structural properties mediate the stability of
640 mutualistic communities. Ecol. Lett., 11, 208-216.
641 61.
642 Peters, D. P. C., Lugo, A. E., Chapin, F. S., Pickett, S. T. A., Duniway, M., Rocha, A. V. et al.
643 (2011). Cross-system comparisons elucidate disturbance complexities and generalities. Ecosphere,
644 2, 1-26.
645 62.
646 Pimm, S. L. (1982). Food Webs. The University of Chicago Press.
647 63.
648 Pimm, S. L. (1984). The complexity and stability of ecosystems. Nature, 307, 321-326.
649 64.
650 Pimm, S. L. (1991). The balance of nature?: ecological issues in the conservation of species and
651 communities. The University of Chicago Press.
652 65.
653 Pimm, S. L. & Lawton, J. H. (1977). Number of trophic levels in ecological communities. Nature,
654 268, 329-331.
655 66.
656 Pimm, S. L., Russell, G. J., Gittleman, J. L. & Brooks, T. M. (1995). The future of biodiversity.
657 Science, 269, 347-350.
658 67.
659 Pimm, S. L., Jenkins, C. N., Abell, R., Brooks, T. M., Gittleman, J. L., Joppa, L. N. et al. (2014).
660 The biodiversity of species and their rates of extinction, distribution, and protection. Science, 344,
661 1246752.
662 68.
27 28 663 Pincebourde, S., Sanford, E., Casas, J. & Helmuth, B. (2012). Temporal coincidence of
664 environmental stress events modulates predation rates. Ecol. Lett., 15, 680-688.
665 69.
666 Quinlan, A. E., Berbés-Blázquez, M., Haider, L. J. & Peterson, G. D. (2016). Measuring and
667 assessing resilience: broadening understanding through multiple disciplinary perspectives. J. Appl.
668 Ecol., 53, 677-687.
669 70.
670 Rockström, J., Steffen, W., Noone, K., Persson, A., Chapin, F. S., Lambin, E. F. et al. (2009). A
671 safe operating space for humanity. Nature, 461, 472-475.
672 71.
673 Rohr, R. P., Saavedra, S. & Bascompte, J. (2014). On the structural stability of mutualistic systems.
674 Science, 345, 416.
675 72.
676 Ruokolainen, L. & Fowler, M. S. (2008). Community extinction patterns in coloured environments.
677 Proc. R. Soc. B., 275, 1775-1783.
678 73.
679 Scheiner, S. M. (2013). The ecological literature, an idea-free distribution. Ecol. Lett., 16, 1421-
680 1423.
681 74.
682 Shou, W., Bergstrom, C. T., Chakraborty, A. K. & Skinner, F. K. (2015). Theory, models and
683 biology. eLife, 4, e07158.
684 75.
685 Solé, R. V. & Montoya, J. M. (2001). Complexity and fragility in ecological networks. Proc. R.
686 Soc. B., 268, 2039-2045.
687 76.
28 29 688 Sousa, W. P. (1984). The role of disturbance in natural communities. Annu. Rev. Ecol. Evol. Syst.,
689 15, 353-391.
690 77.
691 Staniczenko, P. P. A., Lewis, O. T., Jones, N. S. & Reed-Tsochas, F. (2010). Structural dynamics
692 and robustness of food webs. Ecol. Lett., 13, 891-899.
693 78.
694 Steffen, W., Richardson, K., Rockström, J., Cornell, S. E., Fetzer, I., Bennett, E. M. et al. (2015).
695 Planetary boundaries: Guiding human development on a changing planet. Science, 347, 1259855.
696 79.
697 Stenseth, N. C., Durant, J. M., Fowler, M. S., Matthysen, E., Adriaensen, F., Jonzén, N. et al.
698 (2015). Testing for effects of climate change on competitive relationships and coexistence between
699 two bird species. Proc. R. Soc. B, 282, 20141958.
700 80.
701 Stockholm Resilience Centre (2012). Planetary Boundaries: Addressing some key misconceptions.
702 Available at: http://www.stockholmresilience.org/21/research/research-news/7-2-2012-addressing-
703 some-key-misconceptions.html. Last accessed 30 August 2015.
704 81.
705 Suweis, S., Simini, F., Banavar, J. & Maritan, A. (2013). Emergence of structural and dynamical
706 properties of ecological mutualistic networks. Nature, 500, 449-452.
707 82.
708 Tallis, H., Mooney, H., Andelman, S., Balvanera, P., Cramer, W., Karp, D. et al. (2012). A global
709 system for monitoring ecosystem service change. Bioscience, 62, 977-986.
710 83.
711 Tamburello, L., Bulleri, F., Bertocci, I., Maggi, E. & Benedetti-Cecchi, L. (2013). Reddened
712 seascapes: experimentally induced shifts in 1/f spectra of spatial variability in rocky intertidal
713 assemblages. Ecology, 94, 1102-1111.
29 30 714 84.
715 TEEB (2010). The Economics of Ecosystems and Biodiversity: Mainstreaming the Economics of
716 Nature: A Synthesis of the Approach, Conclusions and Recommendations of TEEB.
717 85.
718 Thébault, E. & Fontaine, C. (2010). Stability of ecological communities and the architecture of
719 mutualistic and trophic networks. Science, 329, 853-856.
720 86.
721 Tilman, D., Reich, P. B. & Knops, J. M. H. (2006). Biodiversity and ecosystem stability in a
722 decade-long grassland experiment. Nature, 441, 629-632.
723 87.
724 Tilman, D., Reich, P. B. & Isbell, F. (2012). Biodiversity impacts ecosystem productivity as much
725 as resources, disturbance, or herbivory. Proc. Natl. Acad. Sci. U.S.A., 109, 10394-10397.
726 88.
727 Tylianakis, J. M., Didham, R. K., Bascompte, J. & Wardle, D. A. (2008). Global change and
728 species interactions in terrestrial ecosystems. Ecol. Lett., 11, 1351-1363.
729 89.
730 UN (1992). Text of the CBD. Available at: https://www.cbd.int/convention/text/. Last accessed 30
731 August 2015.
732 90.
733 UN (2008). UN Collaborative Programme on Reducing Emissions from Deforestation and Forest
734 Degradation in Developing Countries (UN-REDD). FAO, UNDP, UNEP Framework Document.
735 91.
736 UN (2010). Aichi Biodiversity Targets. Available at: https://www.cbd.int/sp/targets/. Last accessed
737 30 August 2015.
738 92.
30 31 739 van Nes, E. H. & Scheffer, M. (2004). Large species shifts triggered by small forces. Am. Nat., 164,
740 255-266.
741 93.
742 Walker, B., Holling, C. S., Carpenter, S. R. & Kinzig, A. (2004). Resilience, adaptability and
743 transformability in social–ecological systems. Ecol. Soc., 9, 5.
744 94.
745 Zavaleta, E., Pasari, J., Hulvey, K. & Tilman, G. (2010) Sustaining multiple ecosystem functions in
746 grassland communities requires higher biodiversity. Proc. Natl. Acad. Sci. U.S.A., 107, 1443–1446.
31 32 747 Table 1. International agreements, organisations and agencies whose policy targets and mission and vision statements we searched for terms associated
748 with ecological stability.
Entity Stability related term(s) Document link found
Aichi biodiversity targets (CBD) ‘integrity’; ‘safe ecological http://www.cbd.int/sp/targets/ limits’; ‘resilience’; ‘sustain’; ‘conserve’ Biodiversity International ‘sustain’; ‘safeguard’ http://www.bioversityinternational.org/about-us/who-we-are/ Birdlife International ‘sustain’; ‘maintain’ http://www.birdlife.org/worldwide/partnership/our-vision-mission-and-commitment Convention on Biological Diversity ‘sustain’; ‘conserve’ http://www.cbd.int/convention/articles/default.shtml?a=cbd-01 Conservation International ‘healthy’; ‘sustainable’; http://www.conservation.org/about/Pages/default.aspx#mission ‘stable’ UK Department for Environment, Food & ‘safeguard’ https://www.gov.uk/government/organisations/department-for-environment-food-rural-affairs/about Rural Affairs Diversitas (now rolled into Future Earth) ‘secure’; ‘conserve’; ‘sustain’ http://www.diversitas-international.org/about/mission-and-history Earthwatch ‘sustain’ http://eu.earthwatch.org/about/earthwatch-mission-and-values European Environment Agency ‘sustainable’ http://www.eea.europa.eu/about-us European Platform for Biodiversity Research ‘maintain’; ‘sustain’; http://www.epbrs.org Strategy ‘conserve’ Earth System Science Partnership ‘sustainable’ http://www.essp.org European Union Biodiversity Observation None found http://www.eubon.eu/show/project_2731/ Network Food and Agriculture Organisation ‘security’; ‘sustainable http://www.fao.org/about/en/ Future Earth ‘sustainable’ http://www.futureearth.org Global Environment Facility ‘sustainable’ https://www.thegef.org/gef/whatisgef GreenPeace ‘protect’ http://www.greenpeace.org/international/en/about/our-core-values/ International Association for Landscape ‘altered’ http://www.landscape-ecology.org/index.php?id=14 Ecology Intergovernmental platform on biodiversity ‘conserve’; sustain’ http://dx.doi.org/10.1016/j.cosust.2014.11.002 and ecosystem services Intergovernmental Panel on Climate Change None found http://www.ipcc.ch/organization/organization.shtml International tropical timber organisation ‘sustainable’; ‘conservation’ http://www.itto.int/about_itto/ International Union for Conservation of ‘conserve’; ‘sustain’ http://www.iucn.org Nature LifeWatch infrastructure for biodiversity and None found http://www.lifewatch.eu ecosystem research
32 33 Living with Environmental Change None found http://www.lwec.org.uk/about Natural Capital Project ‘sustainable’ http://www.naturalcapitalproject.org Organisation for Economic Co-operation and ‘sustainable’; ‘resilience’ http://www.oecd.org/env/ Development Rainforest Alliance ‘conserve’; ‘sustain’; http://www.rainforest-alliance.org/about ‘safeguard’ The Economics of Ecosystems and None found http://www.teebweb.org/about/ Biodiversity The Nature Conservancy ‘conserve’ http://www.nature.org/about-us/vision-mission/index.htm?intc=nature.tnav.about.list United Nations Reducing Emissions from ‘constrain impacts’ http://www.un-redd.org Deforestation and Forest Degradation United Nations Convention to Combat ‘sustain’; ‘secure’ http://www.unccd.int/en/Pages/default.aspx Desertification United Nations Environment Programme ‘sustain’ http://www.unep.org/Documents.Multilingual/Default.asp?DocumentID=43 Kyoto protocol (UNFCCC) ‘stabilise’ http://unfccc.int/kyoto_protocol/items/2830.php United Nations Sustainable Development ‘security’; ‘sustainable’; https://sustainabledevelopment.un.org/post2015/transformingourworld Goals ‘resilient’; ‘conserve’; ‘protect’ Wetlands International ‘resilience’ http://www.wetlands.org/Aboutus/VisionMission/tabid/58/Default.aspx World Meteorological Organisation ‘safety’ https://www.wmo.int/pages/about/mission_en.html World Nature Organisation ‘sustainable’ http://www.wno.org/mission Stern Review on the Economics of Climate None found http://mudancasclimaticas.cptec.inpe.br/~rmclima/pdfs/destaques/sternreview_report_complete.pdf Change Worldwatch Institute ‘sustainable’ http://www.worldwatch.org/mission World Wildlife Fund for Nature ‘harmony’; ‘safeguard’ http://wwf.panda.org/wwf_quick_facts.cfm York Environment Sustainability Institute ‘resilient’; ‘maintain’; http://www.york.ac.uk/media/yesi/downloaddocuments/YESI%20Brochure-WEB.pdf ‘conservation’ Convention on International Trade in ‘survival’ http://www.cites.org/eng/disc/what.php Endangered Species of Wild Fauna and Flora International Whaling Commission ‘conservation’ https://iwc.int/history-and-purpose
749
33 34 750 Table 2. Stability-like terms used in policy targets and mission and vision statements of the international agreements, organisations and agencies
751 highlighted in Table 1, ranked in order of frequency of occurrence, and the components of stability that they associate with in the context of their use.
752 The use of resistance here incorporates robustness. We assume that the necessity for systems to be asymptotically stable around an equilibrium point or
753 limit cycle is implicit in the use of every term.
754
Terms used in policy Occurrence Stability component(s) associated most Other associated stability components strongly
‘sustain’/‘sustainable’ 25/42 Persistence Resistance, Resilience, Variability ‘conserve’/‘conservation’ 13/42 Persistence Resistance, Resilience ‘resilience’/‘resilient’ 5/42 Resistance Resilience, Persistence ‘safeguard’ 4/42 Persistence Resistance ‘maintain’ 3/42 Persistence Resistance, Variability ‘secure’/‘security’ 4/42 Persistence Resistance, Resilience ‘stabilise’/‘stable’ 2/42 Variability Resistance, Resilience, Persistence ‘protect’ 2/42 Persistence Resistance ‘altered’ 1/42 Persistence Resistance ‘constrain impacts’ 1/42 Resistance Resilience ‘harmony’ 1/42 Variability ‘healthy’ 1/42 Resistance Resilience ‘integrity’ 1/42 Resistance Persistence, Resilience ‘safety’ 1/42 Resistance Persistence ‘survival’ 1/42 Persistence Resistance, Resilience ‘safe ecological limits’ 1/42 Resistance Persistence, Resilience, Variability, Multiple locally stable equilibria
755
34 35 756 Figure legends
757
758 Fig. 1. Conceptual summary of multifaceted disturbances. Characterisation of pure pulse
759 and press disturbances (a) that are the focus of most theoretical and experimental studies,
760 and an intermediate multiple pulse form of disturbance (dotted blue line) that is also
761 studied frequently, mostly in the form of natural environmental fluctuations in
762 observational studies. Most disturbances are, however, neither pulse nor press and
763 instead change in magnitude over time (b), frequently with shifting mean and variance
764 components. We lack theory and have very limited empirical evidence on the impacts of
765 these directional aspects of disturbances on ecological stability, yet they represent many
766 of the most important and widespread aspects of human impacts (c).
767
768 Fig. 2. The restricted focus of studies on single components of stability (a) and disturbances
769 (b). The total number of studies is slightly lower in (b) because some of the studies we
770 surveyed did not incorporate an explicit disturbance.
771
772 Fig. 3. Overview of studies of ecological stability. Number of studies identified by our
773 survey of the literature that quantified different facets of stability (a), examined the effects
774 of different components of disturbance on those (b), and that used biomass, taxonomic
775 composition or ecosystem functioning as a basis for measuring stability (c).
776
777 Fig. 4. Integrating across multiple dimensions to quantify overall ecological stability. We
778 suggest a method that incorporates multiple stability facets and allows for their differential
779 weighting. This method is based loosely on one developed for the assessment of biodiversity
780 effects on multiple ecosystem functions (Byrnes et al. 2014). A multiple-criteria decision-
781 making approach would also be suitable here. First, the method identifies which stability
35 36 782 facets can be quantified and provides a scoring system for each facet (a). This could be as
783 simple as low, moderate and high, although more sophisticated scoring systems could be
784 developed. It then applies a weighting factor to each score, depending on their perceived
785 relative importance for a given policy or management practice (b). The sum of the weighted
786 scores then corresponds to the stakeholder’s value of the stability of the system (c). Even
787 though different facets of stability may be correlated, there is no need to assume this. Trade-
788 offs and synergies among stability metrics can be incorporated, but the method does not
789 assume dependencies.
36 37 790 Box 1: Why the attempt to define planetary boundaries is flawed
791 Human actions are changing the biosphere in unprecedented ways. One view is that, given the
792 magnitude and novelty of these impacts, there will be thresholds, beyond which abrupt non-linear
793 change will bring the biosphere to a new and undesirable equilibrium. This view of nature, founded
794 upon Holling’s (1973) definition of resilience, explicitly engages policymakers with its invocation
795 of catastrophic tipping points and the conclusion that Earth has already exceeded them. The view is
796 becoming increasingly pervasive in the scientific literature.
797 Certainly, there may be systems that show the tipping points that underpin this worldview.
798 Importantly, there is nothing to suggest they are ubiquitous and so demand their having logical
799 primacy. Nature might work this way sometimes, but there is no compelling argument that it must.
800 In attempting to define global tipping points and, from those, “planetary boundaries”,
801 Rockström et al. (2009) have extended this view to circumstances where it is unlikely to operate.
802 We take as an example the variable they deemed already to be outside the planetary boundary
803 arising from our work (Pimm et al. 1995; Pimm et al. 2014): the rate of species extinctions. The
804 metric is simple — a fraction of species going extinct per unit time. The comparison to a natural
805 background rate is also conceptually easy, though there are practical difficulties (De Vos et al.
806 2015). The notion that the current global species extinction rate — about a thousand times higher
807 than background — has exceeded some tipping point where catastrophic ecological changes must
808 follow is problematical in several ways (Mace et al. 2014).
809 First, it is not clear over what spatial and temporal scales extinction rates have exceeded the
810 boundary. For example, how are the locally high rates of plant and animal extinctions on remote
811 Pacific Islands following first contact with Polynesians and later with Europeans supposed to “tip”
812 processes globally or (say) in the Amazon? And over what time period might these catastrophic
813 changes unfold?
814 Subsequent clarifications by Rockström and colleagues (Stockholm Resilience Centre 2012;
815 Steffen et al. 2015) indicate that the proposed ‘planetary’ boundary for extinctions operates at
37 38 816 regional scales, but they are not explicit in defining either the spatial or temporal extents of these
817 regions. This leaves open the vitally important question for policymakers of what scales are most
818 important.
819 Second, there are models of the consequences of losing species and how many more species
820 will be lost consequently at local and regional scales (Pimm 1991). None shows the kind of
821 runaway processes that Rockström and colleagues imagine. Certainly, there is both an extensive
822 theoretical and empirical literature on how species richness (as opposed to its rate of change) affects
823 a variety of ecosystem functions including primary productivity and nutrient cycling (Loreau et al.
824 2001; Cardinale et al. 2012). This literature shows degradation as species numbers decline
825 (Cardinale et al. 2011), but no clear thresholds.
38 39 826 Box 2: Learning from experience: biodiversity-ecosystem functioning and service provision
827 Even when theoreticians and empiricists converge in what they quantify, there is no guarantee
828 of immediate and successful translation into the policy and management arena. Research on
829 Biodiversity-Ecosystem Functioning (BEF) and Biodiversity-Ecosystem Services (BES)
830 relationships exemplifies this and, as such, we can learn from it.
831 A large body of experiments (> 600 since 1990) developed in close relation with
832 mathematical theory and showed how genetic, species and functional diversity of organisms
833 regulate basic ecological processes – functions – in ecosystems (Cardinale et al. 2012). As a result,
834 there is now unequivocal evidence supported by theory that biodiversity loss reduces biomass
835 production, decomposition and recycling of essential nutrients, and the efficiency at which
836 ecosystems capture biological resources. In parallel, a strong policy impulse developed trying to
837 guarantee the provision of ecosystem services to society, now under the umbrella of the recently
838 established Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services
839 (IPBES; Díaz et al. 2015). Despite the mechanistic understanding of the effects of biodiversity on
840 functioning provided by theoreticians and empiricists, the mechanistic links between biodiversity
841 and ecosystem services are far from being established. This disconnect effectively impairs the
842 distillation of conclusions to inform policy on how biodiversity loss will affect service provisioning
843 and regulation and, ultimately, human wellbeing.
844 An example is Payment for Ecosystem Services (PES), where beneficiaries of nature’s
845 services pay owners or stewards of ecosystems that generate those services. Naeem et al. (2015)
846 suggested recently that few PES studies get the science right, with most projects based on weak
847 scientific foundations. The main reason for this was poor interdisciplinary communication and
848 coordination. The absence of unifying definitions and associated metrics, baseline data, monitoring,
849 recognition of the dynamic nature of ecosystems, and poor interdisciplinary communication and
850 coordination helps to explain this gap. The BEF community measures functions without linking
851 those to known services. The BES community commonly describe services without linking them to
39 40 852 their underlying ecological function. A more active communication and convergence on what to
853 measure and at what scale, and how to monitor over space and time is needed (Cardinale et al.
854 2012; Naeem et al. 2015).
40